Revenue Management under a Nonparametric Ranking Based Choice Model

We consider revenue management problems when customers choose among the offered products according to a nonparametric ranking-based choice model. Under this nonparametric choice model, each customer class is distinguished by a unique ranking of the available products and an arrival probability. Given the arrival of a customer from a particular customer class, this customer will purchase the highest ranking offered product in her respective ranking list. To simplify the revenue management problems that we consider, we restrict the set of customer classes that can exist. Specifically, given a tree where the nodes are the products, we assume that the set of customer classes is derived from paths in the tree, where the order of nodes visited along each potential path gives the corresponding ranking list of a potential customer type. First, we study assortment problems, where the goal is to find a set of products to offer so as to maximize the expected revenue from each customer. We give a dynamic program to obtain the optimal solution. Second, we show how this dynamic programming formulation can be extended to consider the assortment problem when there is a constraint limiting the space consumption of the offered products. Third, we study network revenue management problems, where the goal is to adjust the set of offered products over a selling horizon when the sale of each product consumes a combination of a limited set of resources. A standard linear programming approximation of this problem includes one decision variable for each subset of products. We show that this linear program can be reduced to an equivalent one of substantially smaller size. We give an algorithm to recover the optimal solution to the original linear program from the reduced linear program.